For cost efficiency, you can't beat the commercial white leghorns. They lay their weight in eggs about once a month or less during peak time of the year.
Next in line would be production reds or sexlinks, but the body size of those birds is 50-100% bigger, thus resulting in probably about the same ratio increase in feed consumption.
I find my leghorns good at free range and predator avoidance because they are flighty and VERY aware of their surroundings, with the ability to fly over things if they need to say alive.
For "maximal" production, you'll probably want to go in a 2-3 year cycle and rotate out layers. My oldest leghorn is now 3, and she still lays 5-6 a week. During her prime, she laid 6-7 a week for the first 8 months or so before slowing down. At one point in the first winter, she was laying half of all the eggs we were collecting... and we had 7 brown egg layers who were her age or at most a year older than she was. She was the only white egg layer. Her replacements are doing just as well and I keep them around just for the eggs.